ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স · তারিখ অনির্ধারিত · ২২ প্রশ্ন

১.

Of 132 examinees of a certain school, the ratio of successful to unsuccessful candidates is 9 : 2. If 4 more students passed, what would have been the ratio of successful to unsuccessful students?

ক
21 : 5
খ
18 : 5
গ
23 : 5
ঘ
28 : 5

ব্যাখ্যা

Question: Of 132 examinees of a certain school, the ratio of successful to unsuccessful candidates is 9 : 2. If 4 more students passed, what would have been the ratio of successful to unsuccessful students?

Solution:
successful candidates = (9/11) × 132
= 108

unsuccessful candidates = (2/11) × 132
= 24

new successful candidates = 108 + 4
= 112
new unsuccessful candidates = 24 - 4 = 20

new ratio = 112 : 20
= 28 : 5

২.

Dhruvo has to divide his rectangular field into two parts from one corner to the other using fence. If the area of the field is 540m² and the length of the field is 36m then what will be the length of the fence needed?

ক
32 m
খ
35 m
গ
39 m
ঘ
40 m

ব্যাখ্যা

Question: Dhruvo has to divide his rectangular field into two parts from one corner to the other using fence. If the area of the field is 540m² and the length of the field is 36m then what will be the length of the fence needed?

Solution:
Breadth of the field = 540/36 = 15 m

the length of the fence = diagonal of the field
= √(15² + 36²)
= √1521
= 39 m

৩.

How much time will it take for an amount of Tk. 450 to yield Tk. 81 as interest at 9% per annum of simple interest?

ক
2 years
খ
3 years
গ
4 years
ঘ
None of these

ব্যাখ্যা

Question: How much time will it take for an amount of Tk. 450 to yield Tk. 81 as interest at 9% per annum of simple interest?

Solution:
I = Pnr
⇒ 81 = 450 × n × 9/100
∴ n = (81 × 100)/(450 ×9)
= 2 years

৪.

The difference of the two numbers is 20% of the large number, if the smaller number is 20, then the larger number is-

ক
22
খ
25
গ
30
ঘ
45

ব্যাখ্যা

Question: The difference of the two numbers is 20% of the large number, if the smaller number is 20, then the larger number is-

Solution:
Let the large number be x.
Then,
x - 20 = 20% of x = 20x/100 = x/5
⇒ x - x/5 = 20
⇒ 5x - x = 100
⇒ 4x = 100
∴ x = 25

৫.

If log₁₀(2^m + m - 4) = m(1 - log₁₀5), then m =?

ক
2
খ
3
গ
4
ঘ
5

ব্যাখ্যা

Question: If log₁₀(2^m + m - 4) = m(1 - log₁₀5), then m =?

Solution:
log₁₀(2^m + m - 4) = m(1 - log₁₀5)
⇒ log₁₀(2^m + m - 4) = m(log₁₀10 - log₁₀5)
⇒ log₁₀(2^m + m - 4) = m log₁₀(10/5)
⇒ log₁₀(2^m + m - 4) = mlog₁₀2
⇒ log₁₀(2^m + m - 4) = log₁₀2^m
⇒ 2^m + m - 4 = 2^m
⇒ m = 4

৬.

A train 165 m long is running at a uniform speed of 54 km/hr. How much time will it take to cross a pole?

ক
8 seconds
খ
11 seconds
গ
15 seconds
ঘ
22 seconds

ব্যাখ্যা

Question: A train 165 m long is running at a uniform speed of 54 km/hr. How much time will it take to cross a pole?

Solution:
Speed of train = 54 km/hr
= 54 × 5/18 m/sec
= 15 m/sec

Length of the train = 165 meters

Therefore, time taken by the train to cross a pole = length of train/speed of train
= 165/15 sec
= 11 sec

Thus, train takes 11 seconds to cross the pole.

৭.

If 64% of a number is 2592. What is 88% of that number?

ক
3201
খ
3448
গ
3564
ঘ
None of these

ব্যাখ্যা

Question: If 64% of a number is 2592. What is 88% of that number?

Solution:
let the number be x

64% of x = 2592
⇒ 64x/100 = 2592
⇒ x = (2592 × 100)/64
= 4050

88% of that number = 4050 × 88/100 = 3564

৮.

The average of 4 consecutive numbers is 10.5. The largest of these numbers is:

ক
9
খ
10
গ
11
ঘ
12

ব্যাখ্যা

প্রশ্ন: The average of 4 consecutive numbers is 10.5. The largest of these numbers is:

সমাধান:
৪ টি ক্রমিক সংখ্যার গড় ১০.৫
৪ টি সংখ্যার সমষ্টি = ১০.৫ × ৪ = ৪২

ধরি, সংখ্যাগুলি হল a, a + ১, a + ২, a + ৩
প্রশ্নমতে,
a + a + ১ + a + ২ + a + ৩ = ৪২
⇒ ৪a + ৬ = ৪২
⇒ ৪a = ৪২ - ৬
⇒ ৪a = ৩৬
⇒ a = ৯

∴ বড় সংখ্যাটি হল a + ৩
= ৯ + ৩
= ১২

৯.

What is the greatest number of 3 digits which when divided by 6, 9 and 12 leaves a remainder of 3 in each case?

ক
903
খ
996
গ
975
ঘ
939

ব্যাখ্যা

Questions: What is the greatest number of 3 digits which when divided by 6, 9 and 12 leaves a remainder of 3 in each case?

Solution:
৬, ৯, ১২ এর ল.সা.গু = ৩৬

তিন অঙ্কের বৃহত্তম সংখ্যা = ৯৯৯
৯৯৯ কে ৩৬ দ্বারা ভাগ করলে অবশিষ্ট থাকে ২৭
৯৯৯ - ২৭ = ৯৭২ ; ৩৬ দ্বারা নিঃশেষে বিভাজ্য।

নির্ণেয় সংখ্যা = ৯৭২ + ৩ = ৯৭৫

১০.

Roni is as much younger than Sagar as he is older than Piyal. If the sum of the ages of Piyal and Sagar is 66 years, and Sagar's age is 48 years, then what is the difference between Roni and Piyal's age?

ক
11 years
খ
15 years
গ
25 years
ঘ
30 years

ব্যাখ্যা

Question: Roni is as much younger than Sagar as he is older than Piyal. If the sum of the ages of Piyal and Sagar is 66 years, and Sagar's age is 48 years, then what is the difference between Roni and Piyal's age?

Solution:
Sagar's age is 48 years
the sum of the ages of Piyal and Sagar is 66 years
∴ The age of Piyal is = 66 - 48 year
= 18 year

let, age of Roni is x

48 - x = x - 18
⇒ 2x = 66
∴ x = 33
the difference between Roni and Piyal's age is = 33 - 18
= 15 years

১১.

A sum of money at simple interest amounts to Tk. 815 in 3 years and to Tk. 854 in 4 years. The sum is-

ক
Tk. 500
খ
Tk.525
গ
Tk. 612
ঘ
Tk. 698

ব্যাখ্যা

Question: A sum of money at simple interest amounts to Tk. 815 in 3 years and to Tk. 854 in 4 years. The sum is-

Solution:
Simple interest for 1 year = Tk. (854 - 815)
= Tk. 39

∴ Simple interest for 3 years = Tk.(39 × 3)
= Tk. 117

∴ Sum = (815 - 117)
= Tk. 698

১২.

605 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child receive?

ক
9
খ
11
গ
15
ঘ
Data inadequate

ব্যাখ্যা

Question: 605 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child receive?

Solution:
Let Children = X
A/Q,
605/X = 20% of X
⇒ 605/X = X/5
⇒, X² =5 × 605
⇒ X²= 5² × 11²
X = 55

So each children receive = 605/55
= 11

১৩.

A sum of money at compound interest doubles itself in 15 years. It will become eight times of itself in-

ক
40 years
খ
42 years
গ
45 years
ঘ
50 years

ব্যাখ্যা

Question: A sum of money at compound interest doubles itself in 15 years. It will become eight times of itself in-

Solution:
let the sum P

2P = P (1 + r)¹⁵
⇒ (1 + r)¹⁵ = 2

let, sum will 8 times in n years
8P = P(1 + r)ⁿ
⇒ 8 = (1 + r)ⁿ
⇒ 2³ = (1 + r)ⁿ
⇒ ((1 + r)¹⁵)³ = (1 + r)ⁿ
⇒ (1 + r)⁴⁵ = (1 + r)ⁿ
∴ n = 45 years

১৪.

The weight of an empty bucket is 25% of the weight of the bucket when filled with some liquid. Some of the liquid has been removed. Then, the bucket, along with the remaining liquid, weighed three-fifths of the original weight. What percentage of the liquid has been removed?

ক
40%
খ
(123/2)%
গ
(160/3)%
ঘ
None of the Above

ব্যাখ্যা

Question: The weight of an empty bucket is 25% of the weight of the bucket when filled with some liquid. Some of the liquid has been removed. Then, the bucket, along with the remaining liquid, weighed three-fifths of the original weight. What percentage of the liquid has been removed?

Solution:
let, weight of empty bucket is x liter

x = 25% (x + some liquid)
⇒ x = (1/4) (x + some liquid)
⇒ 4x = x + some liquid
⇒ 3x = some liquid
⇒ some liquid = 3x

Then, the bucket, along with the remaining liquid, weighed three-fifths of the original weight.
weight of removed liquid = (2/5) × 4x = 8x/5

%percentage removed = (8x/5/3x ) × 100%
= (160/3)%

১৫.

A Shopkeeper has 1000 kg of sugar, part of which he sells at 8% and the remaining at 18% profit. He gains 14% on the whole. Find the quantity of sugar that he sold at 8% profit.

ক
600 kg
খ
500 kg
গ
400 kg
ঘ
None of these

ব্যাখ্যা

Question: A Shopkeeper has 1000 kg of sugar, part of which he sells at 8% and the remaining at 18% profit. He gains 14% on the whole. Find the quantity of sugar that he sold at 8% profit.

Solution:
Let,
The cost price of sugar be tk. x per kg
∴ Total cost price = Tk. 1000x
The sugar sold at 8% gain by y kg
The sugar sold at 18% gain by (1000 - y) kg

Now
{(108xy)/100} + [{118x(1000 - y)}/100] = (114/100) × (1000x)
⇒ (108y)/100 + [{118(1000 - y)}/100] = (114 × 1000)/100
⇒ 108y + {118(1000 - y)} = 114 × 1000
⇒ 108y + 118000 - 118y = 114000
⇒ 118000 - 114000 = 10y
⇒ 4000 = 10y
∴ y = 400 kg

১৬.

The perimeter of a rhombus is 56 m and its height is 5 m. Its area is-

ক
50 m²
খ
54 m²
গ
66 m²
ঘ
70 m²

ব্যাখ্যা

Question: The perimeter of a rhombus is 56 m and its height is 5 m. Its area is-

Solution:
one side of rhombus is 56/4 = 14 m

area = 14 × 5
= 70 m²

১৭.

The prime numbers dividing 143 and leaving a remainder of 3 in each are-

ক
5 and 7
খ
2 and 11
গ
3 and 7
ঘ
11 and 13

ব্যাখ্যা

Question: The prime numbers dividing 143 and leaving a remainder of 3 in each are-

Solution:
১৪৩ কে ৭ দ্বারা ভাগ করলে ভাগফল ২০ , ভাগশেষ ৩
১৪৩ কে ৫ দ্বারা ভাগ করলে ভাগফল ২৮, ভাগশেষ ৩

১৮.

Three circles are mutually tangent externally Their centers form a triangle whose sides are of lengths 3, 4, and 5. The total area of the circles (in square units) is-

ক
35π
খ
27π
গ
21π
ঘ
14π

ব্যাখ্যা

Question: Three circles are mutually tangent externally Their centers form a triangle whose sides are of lengths 3, 4, and 5. The total area of the circles (in square units) is-

Solution:
let, the radiuses r₁, r₂, r₃and let r₃>r₂>r₁

ATQ,
r₁ + r₂ = 3
r₁ + r₃ = 4
r₂ + r₃ = 5

r₃ = 5 - r₂

r₁ + 5 - r₂ = 4
⇒ r₂ = r₁ + 1

r₁ + r₁ + 1 = 3
⇒ 2r₁ = 2
∴ r₁ = 1

r₂ = 1 + 1 = 2
r₃ = 5 - 2 = 3

total areas = πr₁² + πr₂² + πr₃²
= π + 4π + 9π
= 14π

১৯.

A started a business with Tk. 2100 and is joined afterwards by B with Tk. 3600. After how many months did B join if the profits at the end of the year are divided equally?

ক
7 months
খ
3 months
গ
4 months
ঘ
5 months

ব্যাখ্যা

Question: A started a business with Tk. 2100 and is joined afterwards by B with Tk. 3600. After how many months did B join if the profits at the end of the year are divided equally?

Solution:
Suppose,
B joined after x months.

Then,
2100 × 12 = 3600 × (12 - x)
⇒ 252 = 432 - 36x
⇒ 36x = 180
∴ x = 5

∴ B joined after 5 months

২০.

25% of Rasel's yearly income is equal to 75% of Aman's monthly income. If Aman's yearly income is 240000 taka. What is Rasel's monthly income?

ক
Tk. 4500
খ
Tk. 6000
গ
Tk. 5000
ঘ
Tk.2300

ব্যাখ্যা

Question: 25% of Rasel's yearly income is equal to 75% of Aman's monthly income. If Aman's yearly income is 240000 taka. What is Rasel's monthly income?

Solution:
Aman's yearly income is 240000 taka
Aman's monthly income is 240000/12 taka
= 20000 taka

75% of Aman's monthly income = 0.75 × 20000 = 15000 taka

25% of Rasel's yearly income = 15000
Rasel's yearly income = 15000 × 4 = 60000 taka

∴ Rasel's monthly income = 60000/12 = Tk. 5000

২১.

An accurate clock shows the time as 3.00. After the hour hand has moved 135°, the time would be-

ক
5 : 30
খ
7 : 30
গ
9 : 30
ঘ
10 : 00

ব্যাখ্যা

Question: An accurate clock shows the time as 3.00. After the hour hand has moved 135°, the time would be-

Solution:
প্রতি ৫ ঘরের মান ৩০°

১৩৫° তে ঘন্টার কাঁটা যায় ৪.৫ ঘর
∴ ৪ ঘন্টা ৩০ মিনিট অতিবাহিত হয়েছে।

নতুন সময় = ৭ : ৩০ মিনিট

২২.

The area of a triangle is 216 cm² and sides are in the ratio 3 : 4 : 5. The perimeter of the triangle is-

ক
12 cm
খ
36 cm
গ
72 cm
ঘ
144 cm

ব্যাখ্যা

Question: The area of a triangle is 216 cm² and sides are in the ratio 3 : 4 : 5. The perimeter of the triangle is-

Solution:
3² + 4² = 5²

It is a right-angled triangle.
let, the sides 3x, 4x, 5x

(1/2) × 3x × 4x = 216
⇒ 12x2 = 432
⇒ x2 = 36
⇒ x = 6

perimeter = (3 × 6) + (4 × 6) + (4 × 6)
= 72 cm